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Interactions between computability theory and set theory

  • Author(s): Schweber, Noah
  • Advisor(s): Montalban, Antonio
  • et al.

In this thesis, we explore connections between computability theory and set theory. We investigate an extension of reverse mathematics to a higher-order context, focusing in particular on determinacy principles, and an extension of computable structure theory to uncountable structures via set-theoretic forcing. We also look at computability-theoretic operations induced by ultrafilters, and the classical computable structure theory of ordinals as clarified by set-theoretic results.

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